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DIALOGUE ON DIALECTICS (WITH REFERENCE TO MATHEMATICS).

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Title: DIALOGUE ON DIALECTICS (WITH REFERENCE TO MATHEMATICS).
Authors: Sayers, Sean, Ernest, Paul, Blunden, Andy, Moore, Alexander, Baldino, Roberto, Larvor, Brendan, Gillies, Donald, Cabral, Tânia C. B.
Source: Philosophy of Mathematics Education Journal. Mar2026, Issue 43, p1-98. 98p.
Subject Terms: Dialectic, Mathematics, Marxist philosophy, Hegelianism, Contradiction, Epistemics
Abstract: The article centers on a comprehensive dialogue among philosophers and scholars—including Sean Sayers, Paul Ernest, Andy Blunden, and others—exploring the nature and application of dialectics with specific reference to mathematics. It examines Hegelian and Marxist dialectical philosophy, emphasizing that all concrete things, including mathematical concepts, are dialectical unities containing contradictions and are in constant flux, challenging traditional logical laws such as the law of identity and non-contradiction. The dialogue addresses the social and historical construction of knowledge and mathematical objects, arguing against Platonic realism and idealism by situating mathematics as a culturally and materially grounded human practice evolving through social discourse and activity. The participants debate the ontological status of objects, concepts, and identity, highlighting the tension between abstract logical principles and lived, changing realities, and propose that dialectics serves as a heuristic and methodological framework for understanding conceptual development, knowledge growth, and cultural practices, including mathematics. [Extracted from the article]
Copyright of Philosophy of Mathematics Education Journal is the property of Paul Ernest, Emeritus Professor at University of Exeter, School of Education & Lifelong Learning and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Education Research Complete
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  Data: DIALOGUE ON DIALECTICS (WITH REFERENCE TO MATHEMATICS).
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  Data: <searchLink fieldCode="JN" term="%22Philosophy+of+Mathematics+Education+Journal%22">Philosophy of Mathematics Education Journal</searchLink>. Mar2026, Issue 43, p1-98. 98p.
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  Data: <searchLink fieldCode="DE" term="%22Dialectic%22">Dialectic</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Marxist+philosophy%22">Marxist philosophy</searchLink><br /><searchLink fieldCode="DE" term="%22Hegelianism%22">Hegelianism</searchLink><br /><searchLink fieldCode="DE" term="%22Contradiction%22">Contradiction</searchLink><br /><searchLink fieldCode="DE" term="%22Epistemics%22">Epistemics</searchLink>
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  Data: The article centers on a comprehensive dialogue among philosophers and scholars—including Sean Sayers, Paul Ernest, Andy Blunden, and others—exploring the nature and application of dialectics with specific reference to mathematics. It examines Hegelian and Marxist dialectical philosophy, emphasizing that all concrete things, including mathematical concepts, are dialectical unities containing contradictions and are in constant flux, challenging traditional logical laws such as the law of identity and non-contradiction. The dialogue addresses the social and historical construction of knowledge and mathematical objects, arguing against Platonic realism and idealism by situating mathematics as a culturally and materially grounded human practice evolving through social discourse and activity. The participants debate the ontological status of objects, concepts, and identity, highlighting the tension between abstract logical principles and lived, changing realities, and propose that dialectics serves as a heuristic and methodological framework for understanding conceptual development, knowledge growth, and cultural practices, including mathematics. [Extracted from the article]
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  Data: <i>Copyright of Philosophy of Mathematics Education Journal is the property of Paul Ernest, Emeritus Professor at University of Exeter, School of Education & Lifelong Learning and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Mathematics
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      – SubjectFull: Marxist philosophy
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      – SubjectFull: Hegelianism
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      – SubjectFull: Epistemics
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              Text: Mar2026
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